scholarly journals Dynamics of a Harvested Prey–Predator Model with Prey Refuge Dependent on Both Species

2018 ◽  
Vol 28 (12) ◽  
pp. 1830040 ◽  
Author(s):  
Md. Manarul Haque ◽  
Sahabuddin Sarwardi
Keyword(s):  
Limit Cycle ◽  
Optimal Harvesting ◽  
Present System ◽  
Prey Refuge ◽  
Bionomic Equilibrium ◽  
Optimal Harvesting Policy ◽  
Equilibrium Level ◽  
Main Observation ◽  
Predator Model

The present paper deals with a prey–predator model with prey refuge in proportion to both species, and the independent harvesting of each species. Our study shows that using refuge as control, it can break the limit cycle of the system and reach the required state of equilibrium level. We have established the optimal harvesting policy. The boundedness, feasibility of interior equilibria and bionomic equilibrium have been determined. The main observation is that the coefficient of refuge plays an important role in regulating the dynamics of the present system. Moreover, the variation of the coefficient of refuge changes the system from stable to unstable and vice-versa. Some numerical illustrations are given in order to support our analytical and theoretical findings.

Prey–predator model for optimal harvesting with functional response incorporating prey refuge

2015 ◽  
Vol 09 (01) ◽  
pp. 1650014 ◽  
Author(s):  
G. S. Mahapatra ◽  
P. Santra
Keyword(s):  
Functional Response ◽  
System Parameter ◽  
Optimal Harvesting ◽  
Functional Responses ◽  
Prey Refuge ◽  
Numerical Examples ◽  
Pictorial Presentation ◽  
Constant Form ◽  
Predator Model ◽  
Predator System

This paper presents a prey–predator model considering the predator interacting with non-refuges prey by class of functional responses. Here we also consider harvesting for only non-refuges prey. We discuss the equilibria of the model, and their stability for hiding prey either in constant form or proportional to the densities of prey population. We also investigate various possibilities of bionomic equilibrium and optimal harvesting policy. Finally we present numerical examples with pictorial presentation of the various effects of the prey–predator system parameter.

STABILITY AND BIFURCATION ANALYSIS OF A DISCRETE PREY–PREDATOR MODEL WITH SQUARE-ROOT FUNCTIONAL RESPONSE AND OPTIMAL HARVESTING

2020 ◽  
Vol 28 (01) ◽  
pp. 91-110
Author(s):  
PRABIR CHAKRABORTY ◽  
UTTAM GHOSH ◽  
SUSMITA SARKAR
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Functional Response ◽  
Population Model ◽  
Optimal Harvesting ◽  
Herd Behavior ◽  
Square Root ◽  
Optimal Harvesting Policy ◽  
Optimal Value ◽  
Predator Model

In this paper, we have considered a discrete prey–predator model with square-root functional response and optimal harvesting policy. This type of functional response is used to study the dynamics of the prey–predator model where the prey population exhibits herd behavior, i.e., the interaction between prey and predator occurs along the boundary of the population. The considered population model has three fixed points; one is trivial, the second one is axial and the last one is an interior fixed point. The first two fixed points are always feasible but the last one depends on the parameter value. The interior fixed point experiences the flip and Neimark–Sacker bifurcations depending on the predator harvesting coefficient. Finally, an optimal harvesting policy has been introduced and the optimal value of the harvesting coefficient is determined.

scholarly journals Optimal harvesting policy of a prey–predator model with Crowley–Martin-type functional response and stage structure in the predator

2018 ◽  
Vol 23 (4) ◽  
pp. 493-514 ◽  
Author(s):  
Balram Dubey ◽  
Shikhar Agarwal ◽  
Ankit Kumar
Keyword(s):  
Three Dimensional ◽  
Stage Structure ◽  
Optimal Level ◽  
Effective Control ◽  
Optimal Harvesting ◽  
Catch Per Unit Effort ◽  
Optimal Harvesting Policy ◽  
Control Instrument ◽  
Long Time ◽  
Predator Model

In this paper, a three-dimensional dynamical model consisting of a prey, a mature predator, and an immature predator is proposed and analysed. The interaction between prey and mature predator is assumed to be of the Crowley–Martin type, and both the prey and mature predator are harvested according to catch-per-unit-effort (CPUE) hypothesis. Steady state of the system is obtained, stability analysis (local and global both) are discussed to explore the long-time behaviour of the system. The optimal harvesting policy is also discussed with the help of Pontryagin's maximum principle. The harvesting effort is taken as an effective control instrument to preserve prey and predator and to maintain them at an optimal level.

MODELING PREY-PREDATOR TYPE FISHERY WITH RESERVE AREA

2010 ◽  
Vol 03 (03) ◽  
pp. 351-365 ◽  
Author(s):  
MINI GHOSH
Keyword(s):  
Maximum Yield ◽  
Optimal Harvesting ◽  
Prey Refuge ◽  
Bionomic Equilibrium ◽  
Reserve Area ◽  
Fishery Model

This paper presents a prey-predator type fishery model in two patch environment. We assume that one patch is accessible to both prey and predator while other is a refuge for prey. The prey refuge constitutes a reserve zone where fishing is not allowed. In the unreserved area there are both prey and predators and harvesting of only predators is permitted. The equilibria of the model and their stability are discussed. Also we investigate various possibilities of bionomic equilibrium. Finally, the model is simulated for varied set of parameters and sensitivity of the parameters and effect of the size of reserve on maximum yield are studied. We found that it is the best to keep the size of reserve small and increase the harvesting effort upto optimal harvesting effort to get the higher maximum yield.

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